o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - - - September 7, 1995 - - O P - S F N E T Volume 2, Number 5 - - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - Tom H. Koornwinder, Editor thk@fwi.uva.nl - - - - - - The Electronic News Net of the SIAM Activity Group - - on Orthogonal Polynomials and Special Functions - - - - Please send contributions to: poly@siam.org - - & address changes to: poly-request@siam.org - - - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o Today's Topics: 1. Newsletter will appear again 2. Election of new officers 3. Problems in getting subscribed to OP-SF Net 4. Minisymposium at SIAM Annual Meeting in Charlotte 5. International Conference on Harmonic Analysis, Delhi, India 6. Report on conference in honour of Lee Lorch 7. Macdonald-Stanley conjecture for Jack polynomials solved (weakly) 8. Death of S. Chandrasekhar 9. Szego bust 10. Proceedings of hypergroups conference 11. New book on Heun's differential equations 12. Early history of Bessel functions 13. Tenure track position in Bogota (Columbia) 14. Looking for a position 15. ftp and WWW addresses 16. Changes of address 17. Obtaining back issues of OP-SF Net Calendar of events: see issue/topic: 1995 October 25: Minisymposium at SIAM Annual Meeting in Charlotte 2.5 #4 November 27- December 1: main topic q-special functions in fourth week of Warsaw Minisemester on Quantum groups and quantum spaces: 2.4 #4 December 18-22: International Conference on Harmonic Analysis, Delhi 2.5 #5 1996 April 22-23: Umbral Calculus Special Session at MIT 2.4 #5 May 6-26: CRM Workshop on the Theory of Special Functions 2.1 #5 July 1-5: Meeting in Canterbury on Symmetries and Integrability of Difference Equations 2.4 #6 August, last week: Workshop Transform Methods & Special Functions 2.4 #7 Topic #1 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: Newsletter will appear again As already announced in OP-SF Net 2.4, Topic #1, Wolfram Koepf is the new editor of the printed Newsletter of our Activity Group. The Newsletter will appear every four months, in October 1995 (submission deadline September 15) and in February and June 1996. Wolfram Koepf welcomes Newsletter contributions, preferably by email and in Latex format. Other formats are also acceptable and can be submitted by email, regular mail or fax. The editor's address is: Wolfram Koepf Konrad-Zuse-Zentrum Heilbronner Str. 10, D-10711 Berlin, Germany tel.: +49-30-896 04-216 fax: +49-30-896 04-125, email: koepf@zib-berlin.de Topic #2 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Charles F. Dunkl Subject: Election of new officers Members of the Activity group will soon receive ballot forms for election of new officers of our Activity Group. The candidates are: chair: Charles Dunkl, unopposed vice-chair: Tom Koornwinder, unopposed secretary: Daniel Lozier and Nico Temme program chair: Willard Miller, Jr. and Alan Schwartz Topic #3 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: Problems in getting subscribed to OP-SF Net There have been some complaints in the past from people subscribing to OP-SF Net and getting no reply. SIAM is working on a new procedure for handling requests for subscription. In the meantime, if anyone has complaints, please contact Diane Fryer at SIAM or me . Topic #4 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Martin Muldoon (Program Director) Subject: Minisymposium at SIAM Annual Meeting in Charlotte We remind you (see OP-SF Net 2.3, Topic #8) that our Activity Group will sponsor a Minisymposium "Computational Aspects of Special Functions and Orthogonal Polynomials" at the SIAM Annual Meeting in Charlotte, North Carolina, October 23-26, 1995. The Minisymposium will take place on Wednesday, October 25, 5.00-7.30 p.m. The organizer is Martin E. Muldoon (York University, Canada). The program is as follows: 5.00 John P. Boyd (University of Michigan, Ann Arbor, MI), "Numerical verification of exponential asymptotics via a Chebyshev polynomial pseudospectral algorithm in multiple precision: radiation coefficient of a weakly nonlocal solitary wave" 5.30 Charles F. Dunkl (University of Virginia, Charlottesville, VA), "Hyperelliptic integrals, the surface measure of ellipsoids, and response surfaces" (with Donald E. Ramirez) 6.00 Walter Gautschi (Purdue University, West Lafayette, IN), "Computing orthogonal polynomials of Sobolev type" 6.30 Daniel W. Lozier (National Institute of Standards and Technology, Gaithersburg, MD), "Software issues in the computation of special functions" 7.00 Nico M. Temme (CWI, Amsterdam), "Large parameter evaluations of some classical distribution functions" For registration, see the Preliminary Program of the SIAM Annual Meeting sent to all SIAM members, or see WWW: http://www.siam.org or send an email to meeting@siam.org Topic #5 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: A.I. Singh Subject: International Conference on Harmonic Analysis, Delhi, India An International Conference on Harmonic Analysis will be organized at the Department of Mathematics, University of Delhi, Delhi-110007, India from 18th to 22nd December, 1995. The programme will include special talks on different aspects of harmonic analysis such as measure algebras, homomorphisms, multipliers, positive definite functions, spectral synthesis and H-spaces. A series of expository lectures on Hypergroups by Professors K.A. Ross, A.L. Schwartz and others will be a special feature of the conference. For further information please contact: Prof.(Mrs> Ajit Iqbal Singh Department of Mathematics University of Delhi Delhi-7, India fax: +91-11-725 7011 Topic #6 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Walter Van Assche Subject: Report on conference in honour of Lee Lorch (A slightly longer report by Walter Van Assche will appear in the Newsletter) In September 1995, Lee Lorch will celebrate his eightieth birthday. For this occasion, a conference was organized at York University (Canada) on June 9 and 10, 1995. Some forty people were present and attended various talks on mathematical topics of interest to Lee Lorch, but also talks related to the societal topics in which Lee always has had active interest. One of Lee's mathematical interests has been the monotonicity properties of zeros of Bessel functions or functions of a similar nature. A basic method for studying monotonicity properties of zeros of special functions is Sturm's method, for which there is a continuous version (for zeros of the solution of a Sturm-Liouville differential operator) and there is also a discrete version for polynomials which form a Sturm sequence (a three-term recurrence with a particular sign property). Lee Lorch's main contributions can be found in joint papers with Peter Szego and Martin Muldoon. Lee also had an continuing interest in Lebesgue constants and various methods of summability. On the first day of the conference (June 9, 1995) there were one hour talks by Richard Askey on "Bessel functions and how to use them when considering more general classes of functions" and Cora Sadosky on "Restricted BMO in products spaces". There were also some 30 minute talks by P.G. Rooney, Walter Van Assche, Angelo Mingarelli, A. McD. Mercer, Mark Ashbaugh, Mourad Ismail, James A. Donaldson, and Arpad Elbert dealing with Hankel transforms, zeros of orthogonal polynomials, eigenvalues of matrices and differential operators, Bessel functions and isoperimetric inequalities, integral operators and $q$-Sturm-Liouville problems, and linear shallow water theory. The morning of the second day of the conference was still devoted to mathematics with one hour talks by Roderick Wong on "Asymptotics and special functions", Jean-Pierre Kahane on "Summability, order and products of Dirichlet series", and 30 minute talks by Dennis Russell and Mark Pinsky on Fourier transforms and Fourier integrals in several variables. In the afternoon there was a nice talk by Donald J. Newman with a beautiful proof of the Morley triangle theorem: Let ABC be an arbitrary triangle with vertices at the points A, B, C. Construct a new triangle (the Morley triangle) by trisecting the angles alpha, beta and gamma at respectively A, B and C inside the triangle ABC and by taking the first intersection points as the vertices of the new triangle. Then this Morley triangle is always an equilateral triangle. There was also a 30 minute talk by Amram Meir on random trees, and the rest of the afternoon of June 10 was devoted to Lee's societal contributions for which he has become well-known, with talks by Chandler Davis, Mary Gray, and Johnny Houston pointing out the "Contributions of Lee Lorch to expanding access to mathematics", showing that Lee Lorch is "A mathematician who cares". Finally, the conference was closed with a dinner during which Lee was awarded the Lifetime Achievement Award of the National Association of Mathematicians by Jack Alexander, president of the Association. Topic #7 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From; OP-SF Net editor Subject: Macdonald-Stanley conjecture for Jack polynomials solved (weakly) This item is partially based on email communications by Doron Zeilberger and by Luc Vinet . Many conjectures involving the Jack polynomials have been formulated. A famous one is due to I.G. Macdonald and is reproduced in R.P. Stanley's reference article "Some combinatorial properties of Jack symmetric functions, Adv. in Math. 77 (1988), 76-115. Roughly, it states the following. Let J_lambda(x;alpha) be the Jack polynomial in the variables x=(x_1,...,x_n) and with parameter alpha. Let the v_{lambda,mu} be its expansion coefficients in terms of the symmetric monomials m_mu(x). It is conjectured that these expansion coefficients, when suitably normalized, are polynomials in alpha with nonnegative integer coefficients. Recently, Luc Lapointe and Luc Vinet proved a weak form of the Macdonald-Stanley conjecture: the suitably normalized coefficients are polynomials in alpha with integer coefficients. They obtained this result by first deriving a Rodrigues type formula for the Jack polynomials. This Rodrigues type formula involves so-called creation operators which are built from Dunkl operators. The full proof of the Rodrigues type formula is given in: L. Lapointe & L. Vinet, Exact operator solution of the Calogero-Sutherland model, CRM preprint #2272, electronically available as q-alg 9509003 or from WWW: http://www.crm.umontreal.ca A brief announcement of the Rodrigues type formula together with a proof of the weak form of the Macdonald-Stanley conjecture is given in: L. Lapointe & L. Vinet, A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture, CRM preprint #2294, electronically available as q-alg 9509002 or from WWW: http://www.crm.umontreal.ca This paper will appear soon in the International Mathematics Research Notices. To see the Lapointe-Vinet proof in action see Doron Zeilberger's Maple program LUC, obtainable from WWW: http://www.math.temple.edu/~zeilberg Doron Zeilberger adds that he has further news from Adriano Garsia: Garsia can prove a similar polynomiality conjecture for the Macdonald polynomials associated with root system A_n. Topic #8 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: Death of S. Chandrasekhar (With thanks to Dick Askey, Willard Miller and Ernie Kalnins for providing information) Prof. S. Chandrasekhar died on August 22, 1995 at the age of 84. He was born in Lahore, India and he studied at the University of Madras, India and at Trinity College, Cambridge, England. He worked at the University of Chicago. He is well known for his work in theoretical astronomy, see for instance his book "The mathematical theory of black holes", Oxford University Press, 1983. This book left unanswered questions about the intrinsic characterisation of the explicit solutions of the spinor equations of mathematical physics in the curved background of a rotating black hole (Kerr space time). In this problem the so called Teukolsky functions play a crucial role. These functions are confluent forms of the solutions of the most general linear homogeneous ordinary differential equation of second order with four regular singularities, viz. Heun's equation. Significant progress in the solution of this problem was made by E.G. Kalnins, W. Miller, Jr., and G.C. Williams. This summer Chandrasekhar's last book appeared, "Newton's `Principia' for the common reader", Oxford University Press, 1995. Further information on his life can be found in the biography "Chandra" by Kameshwar C. Wali, University of Chicago Press, 1991. Topic #9 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Paul Nevai Subject: Szego bust The dedication of the Szego bust (see OP-SF Net 2.2, Topic #8) took place on Wednesday, August 23, 1995, in Kunhegyes, Hungary, in front of roughly a hundred people, including about 30 mathematicians + Veronica & Steve Tincher (Szego's daughter and grandson). I like the statue (bust + pedestal) a lot. The dedication ceremony was very nicely done. The additional two copies will be done by the end of September. Thanks again to all who generously supported this project. (A longer account of this ceremony, written by Kathy A. Driver and edited by Paul Nevai, is available from Paul Nevai on request.) Topic #10 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: Proceedings of hypergroups conference The following book was already briefly mentioned in OP-SF Net 2.3, Topic #14. Applications of Hypergroups and Related Measure Algebras William C. Connett, Marc-Olivier Gebuhrer, and Alan L. Schwartz (eds.) Contemporary Mathematics, 183 American Mathematical Society, 1995 441 pages (softcover) ISBN 0-8218-0297-6 About the conference: The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. They talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks. About the proceedings: Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work. Contents: N. Ben Salem and M.N. Lazhari, Limit theorems for some hypergroup structures on R^n x [0,infinity[ Yu. M. Berezansky, Nuclear spaces of test functions connected with hypercomplex systems and representations of such systems Yu. M. Berezansky and A.A. Kalyuzhnyi, Hypercomplex systems and hypergroups: Connections and distinctions W.R. Bloom and Z. Xu, The Hardy-Littlewood maximal function for Chebli-Trimeche hypergroups H. Chebli, Sturm-Liouville hypergroups W.C. Connett and A.L. Schwartz, Continuous 2-variable polynomial hypergroups P. Eymard, A survey of Fourier algebras A. Fitouhi and M.M. Hamza, Expansion in series of Laguerre functions for solution of perturbed Laguerre equations L. Gallardo, Asymptotic behaviour of the paths of random walks on some commutative hypergroups M.-O. Gebuhrer, Bounded measures algebras: A fixed point approach H. Heyer, Progress in the theory of probability on hypergroups T.H. Koornwinder, Discrete hypergroups associated with compact quantum Gelfand pairs B.M. Levitan, Transmutation operators and the inverse spectral problem M. Mabrouki, Limit theorems for the spin process N.H. Mahmoud, Differential operators with matrix coefficients and transmutations B.P. Osilenker, Generalized product formulas for orthogonal polynomials G.B. Podkolzin, An infinitesimal algebra of the hypergroup generated by double cosets and nonlinear differential equations M. Rosler, Convolution algebras which are not necessarily positivity-preserving K.A. Ross, Signed hypergroups - A survey V.S. Sunder, On the relation between subfactors and hypergroups R. Szwarc, Connection coefficients of orthogonal polynomials with applications to classical orthogonal polynomials K. Trimeche, Generalized transmutation and translation operators associated with partial differential operators L. Vainerman, Gel'fand pairs of quantum groups, hypergroups and q-special functions M. Voit, Central limit theorems for Jacobi hypergroups N.J. Wildberger, Finite commutative hypergroups and applications from group theory to conformal field theory Topic #11 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Andre Ronveaux Subject: New book on Heun's differential equations The following book will appear in October 1995: Heun's Differential Equations Andre Ronveaux (ed.) with contributions by F.M. Arscott, S.Yu. Slavyanov. D. Schmidt, G. Wolf, P. Maroni and A. Duval Oxford University Press, October 1995, 368 pages, IBSN 859695-2 About the book: Heun's equation is a linear second-order differential equation which occurs in a wide range of problems in applied mathematics. This differential equation with four regular singular points generates by confluence four different differential equations. Areas in which these equations occur include the integral equations of potential theory, wave propagation, electrostatic oscillation, and Schrodinger's equation. A recent symposium on the topic surveyed both the current theory and also the main areas of application. The book is a commissioned collection of edited papers from contributors to the symposium. Topic #12 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Walter Van Assche Subject: Early history of Bessel functions Here's a reference that may be (should be) of interest to you: Jacques Dutka: "On the early history of Bessel functions", Archive for the History of Exact Sciences 49 (1995), No.2, 105-134. Topic #13 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: Jairo Charris Subject: Tenure track position in Bogota (Columbia) The Mathematics Department at the National University of Colombia in Bogota is trying to push forward its Ph.D. Program in Mathematics. In order to attract competent new faculty members, it announces an international competition for regular faculty positions. The selection is based only on the evaluation of the curriculum vitae, on publications, on letters of recommendation of known mathematicians and on a proposal of the activity he plans to carry out in Colombia. It is open to a Ph.D aged 25 to 45 with very good promise or experience in research represented by papers published in known journals and strong commitment of teaching at the Ph.D. level. Willingness to help students with their dissertations is very much desirable. The selected candidates will be granted an initial contract of one year at the associate professor level. The salary is close to US $ 1,600 a month (after taxes) but payment is for 15 months a year (This is equivalent to about US $ 2,200 a month stipend in the USA). The nature of the position is tenure track, but there is a one year probation period and a Faculty evaluation of performance at the end of that period. The candidate does not have to know Spanish. However, Spanish is the official language in Colombia and it is expected the winners of the contest will learn some Spanish during their first year in Colombia. Some work at the Department is being done in Special Functions, Orthogonal Polynomials, Approximation Theory and related areas. However, Partial Differential Equations, Logic, Category Theory, Lie Algebras and Lie Groups also belong to its priorities. For further information please contact Jairo Charris Department of Mathematics Universidad Nacional de Colombia Santafe de Bogota Colombia email: demat125@ciencias.campus.unal.edu.co Topic #14 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: S. Yakubovich Subject: Looking for a position Dr. S. Yakubovich from Minsk (Belarus) is urgently looking for a (regular or visiting) position or a research grant in Mathematical Analysis and Applications. He is a specialist in the Theory of Functions, Integral Transforms and Special Functions. He is also experienced in programming (including computer algebra) and implementing results on special functions. He was a coauthor of three monographs on these topics and he published more that 60 research papers. He is 34 years old and he has a family with two children. More detailed information can be provided on request. Any suggestions about possible openings are welcome. Please contact: e-mail: semen@mmf.bsu.minsk.by Fax: +7-0172-265 940 Mail address: P.O.Box 385 Minsk-50 220050 Belarus (Net Editor's note: Topics like this one will only be published in OP-SF Net in exceptional cases: in the case of unemployed researchers with a certain reputation in the field of Orthogonal Polynomials and Special Functions, as should be evident from the list of publications.) Topic #15 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: ftp and WWW addresses The list of ftp and WWW addresses relevant for our field, see OP-SF Net 2.4, Topic #22, remains available at ftp: ftp.fwi.uva.nl directory: pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir, file: WWWaddresses This file will be regularly updated, and the changes will be mentioned in OP-SF Net. Please mail corrections and additions for this list to me . Compared to the list in OP-SF Net 2.4, there are the following changes and additions: MathSciNet (demo version of Math. Reviews online): WWW: http://www.ams.org/web/mathscinet/msn-home.html AMS preprint server: WWW: http://e-math.ams.org/web/preprints/preprints-home.html Centre de Recherches Mathematic, Montreal (a.o. Vinet): WWW: http://www.crm.umontreal.ca Topic #16 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: Changes of address The address of Willard Miller at the University of Minnesota changed to: Willard Miller, Jr. Professor and Acting Dean Institute of Technology, University of Minnesota 105 Walter Library, 117 Pleasant Street S.E. Minneapolis, Minnesota 55455 miller@ima.umn.edu 612-624-2006 FAX: 612-624-2841 Marcel de Jeu, who is working in the area of special functions associated with root systems, will stay in Paris (Universite Paris 7, to start with) until February 1, 1996. His address there is: Marcel de Jeu 56 rue Oberkampf 75011 Paris France Tel.: +33-1 4338 7735 e-mail: dejeu@mathp7.jussieu.fr Tom Koornwinder will stay during the period October 2 - November 23, 1995 at the Mittag Leffler Institute near Stockholm, Sweden. Mathijs Dijkhuizen (working on special functions in connection with quantum groups), has returned from Kobe (Japan) and will also stay at the Mittag Leffler Institute during October and November. The address for both will be: Institut Mittag Leffler Aurav\"agen 17 S-182 62 Djursholm Sweden tel. +46-8-755 1809 fax +46-8-755 9971 Topic #17 --------------- OP-SF NET --------------- September 7, 1995 ~~~~~~~~~ From: OP-SF Net editor Subject: Obtaining back issues of OP-SF Net Back issues of OP-SF Net can be obtained from ftp: ftp.fwi.uva.nl, in directory pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir or WWW: http://math.ohio-state.edu/JAT Contributions to the OP-SF Net 2.6 should reach the email address poly@siam.org before November 1, 1995. In order to join the SIAM Activity Group on Orthogonal Polynomials and Special Functions, and thereby receive the Newsletter, you have to become a member of SIAM. The annual dues are $93 for SIAM plus $10 for the Group. Contact the email address service@siam.org. o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - OP-SF Net is a forum of the SIAM Activity Group on - - Special Functions and Orthogonal Polynomials. - - We disseminate your contributions on anything of interest to the - - special functions and orthogonal polynomials community. This - - includes announcements of conferences, forthcoming books, new - - software, electronic archives, research questions, job openings. - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - Send submissions to: poly@siam.org - - Send address changes to: poly-request@siam.org - - Get back issues by ftp from: ftp.fwi.uva.nl, in directory - - pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir - - Information on joining SIAM - - and this activity group: service@siam.org - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - The Officers of the Activity Group are: - - Charles Dunkl, Chair - - George Gasper, Vice Chair - - Tom H. Koornwinder, Secretary and OP-SF Net Editor - - Martin E. Muldoon, Program Director - - Newsletter Editor is: - - Wolfram Koepf - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o